A wave pulse travelling to the right along a thin cord reaches a discontinuity w
ID: 1634368 • Letter: A
Question
A wave pulse travelling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses? (a) Both are right side up (b) The reflected pulse returns right side up while the transmitted pulse is inverted. (c) The reflected pulse returns inverted while the transmitted pulse is right side up (d) Both are inverted (e) It is impossible to predict. A cello A-string vibrates in its first normal mode with a frequency f_o = 220 Hz. The vibrating segment is L = 70 cm long and has a mass m = 1.2g. (a) Find the tension in the string. (b) Determine the frequency of vibration when the string vibrates in three segments. (c) Assuming that in part (b) the amplitude of the standing wave at an antinode is A = 0.4 mm, calculate the maximum transverse velocity of the string at this point.Explanation / Answer
1)
c) The reflected pulse returns inverted while the transmitted pulse is right side up.
This is because a tight end would cause an inverted reflection and an open end would cause a right-side-up reflection. The transition to a heavier rope, in this example, is closer to the “tight end” condition: an infinitely heavy rope would be equivalent to the perfectly tight end. Therefore, the reflection will be inverted. The transmitted pulse is right-side-up in any case, because of vertical momentum conservation.